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af-algebras

Proceedings of the London Mathematical Society (1)

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Fourier invariant partially approximating subalgebras of the irrational rotation C*-algebra
S. Walters
Journal:

Proceedings of the London Mathematical Society / Volume 88 / Issue 2 / March 2004

Published online by Cambridge University Press:

08 March 2004, pp. 505-525

Print publication:

March 2004
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For a dense $G_\delta$-set of parameters, the irrational rotation algebra is shown to contain infinitely many C*-subalgebras satisfying the following properties. Each subalgebra is isomorphic to a direct sum of two matrix algebras of the same (perfect square) dimension; the Fourier transform maps each summand onto the other; the corresponding unit projection is approximately central; the compressions of the canonical generators of the irrational rotation algebra are approximately contained in the subalgebra.